Finite Group Databasebeta

← #14437806

Subgroups — #14437806

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752672C211yesmaximal, characteristic
2#11752506C211yesmaximal, characteristic, complemented
3#11750782C211yesmaximal, characteristic, complemented
4C5×#4694C211yesmaximal, characteristic, complemented
5C3×C4×C8×D5C211yesmaximal, characteristic, complemented
6#11748135C214yesmaximal, complemented
7#11747963C214yesmaximal, complemented
8#11746930C211yesmaximal, characteristic, complemented
9#11746906C211yesmaximal, characteristic, complemented
10#10613293—31nomaximal, Hall
11C2×#6772C2212yes—
12#91758C2211yescharacteristic
13#91758C2211yescharacteristic
14C5×#874C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C2×C3×C8×D5C2212yes—
17C3×C42×D5C2211yescharacteristic
18#91449—21no—
19#91449—21no—
20Dic5×D12—21no—
21Dic5×D12—21no—
22#91388C2212yes—
23#91373C2212yes—
24#91360—21no—
25#91359—21no—
26#91358C2212yes—
27#91333—21no—
28Dic5×Dic6—21no—
29C3×C4×C5×C8C2211yescharacteristic
30#91100C2214yes—
31C5×#821C2214yes—
32C3×C8×Dic5C2212yes—
33C3×C4×#168C2211yescharacteristic
34#90975C2214yes—
35#90967C2214yes—
36#78463—51nomaximal, Hall
37#66062—31no—
38#66050—31no—
39C5×#486—31no—
40#65382—31no—
41#65359—31no—
42#65061—34no—
43#65057—34no—
44C4×C8×D5D311yescharacteristic, complemented
45#64970—31no—
46C2×Dic30—21no—
47C2×Dic30C2312yes—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C5×D12C2312yes—
51C2×C5×Dic6—21no—
52C2×C3×C4×D5D411yescharacteristic
53C2×C3×C4×D5D411yescharacteristic
54C2×C3×C4×D5C2311yescharacteristic
55C2×#1201—22no—
56C2×D3×Dic5—22no—
57#6772—28no—
58C2×C3×C5×C8C2312yes—
59C3×C42×C5C2311yescharacteristic
60C4⋊Dic15—21no—
61C4⋊Dic15—21no—
62C4⋊Dic15—21no—
63C4⋊Dic15C2312yes—
64C5×C4⋊Dic3—21no—
65C5×C4⋊Dic3C2312yes—
66C3×C4×Dic5D411yescharacteristic
67C3×C4×Dic5D411yescharacteristic
68C3×C4×Dic5C2311yescharacteristic
69C2×C3×#168C2312yes—
70C3×C8×D5—24no—
71Dic3⋊Dic5—22no—
72#6669—22no—
73(C2×D3)⋊Dic5—22no—
74(C2×D3)⋊Dic5—22no—
75#6665—22no—
76Dic3×Dic5—22no—
77#5477—51no—
78#5470—51no—
79C2×C3×C4×C8—51no—
80#5113—54no—
81#4697—54no—
82#4694—51no—
83#4694D511yescharacteristic, complemented
84#4681—51no—
85#4681—51no—
86C2×#711—32no—
87C5×C4⋊Q8—31no—
88C5×#127—31no—
89#4092—61no—
90Q8×Dic5—61no—
91#4084—61no—
92#4084—61no—
93#4082—32no—
94D4×Dic5—61no—
95D4×Dic5—61no—
96C2×C8×D5C2×D312yes—
97#4043—61no—
98#4038—32no—
99#4036—32no—
100#4033—61no—
101C42×D5C2×D311yescharacteristic
102#4015—31no—
103#4015—31no—
104C5×#102—34no—
105C4×C5×C8C2×D311yescharacteristic
106#3964—34no—
107#3948—34no—
108C8×Dic5C2×D312yes—
109#3942—34no—
110C4×#168C2×D311yescharacteristic
111#3131—151noSylow
112C22×C5×D3—22no—
113C22×C3×D5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2411yescharacteristic
117C2×Dic15—22no—
118C2×Dic15—22no—
119Dic30—24no—
120Dic30—42no—
121C2×C5×Dic3—22no—
122C5×D12—24no—
123C5×D12—42no—
124C5×D12—42no—
125C5×Dic6—42no—
126C2×C3×Dic5C2×D411yescharacteristic
127C2×C3×Dic5C2×D411yescharacteristic
128C2×C3×Dic5C2×D411yescharacteristic
129C3×C4×D5—22no—
130C3×C4×D5—22no—
131C3×C4×D5#4114yes—
132#1201—44no—
133D3×Dic5—44no—
134C3×C5×C8—22no—
135C3×#168—22no—
136C2×#235—52no—
137C22×C3×C8—52no—
138C2×C3×C42—51no—
139#930—101no—
140#930—101no—
141#926—52no—
142#924—101no—
143#924—101no—
144#875—52no—
145#874C2×D511yescharacteristic
146C4×D12—101no—
147C4×D12—101no—
148#870—52no—
149#869—51no—
150#869—51no—
151#869C2×D511yescharacteristic
152C4×Dic6—101no—
153C4×Dic6—101no—
154C3×C4×C8—52no—
155C3×C4×C8—51no—
156C3×C4×C8C2×D511yescharacteristic
157#821—54no—
158#821C2×D514yes—
159#816—54no—
160#816—54no—
161C2×C5×Q8—61no—
162C2×C5×D4—32no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C22⋊D5—62no—
166C22×Dic5—62no—
167#711—68no—
168C2×C4×D5D1211yescharacteristic
169C2×C4×D5D1211yescharacteristic
170C2×C4×D5C22×D311yescharacteristic
171C2×Dic10—32no—
172C2×Dic10—61no—
173C2×C5×C8C22×D312yes—
174C5×C4⋊C4—32no—
175C5×C4⋊C4—61no—
176C42×C5C22×D311yescharacteristic
177C22⋊Dic5—62no—
178C22⋊Dic5—62no—
179#685—62no—
180C4⋊Dic5—32no—
181C4⋊Dic5—61no—
182C4⋊Dic5—61no—
183C4⋊Dic5—61no—
184C4⋊Dic5—62no—
185#683—62no—
186C4×Dic5—62no—
187C4×Dic5D1211yescharacteristic
188C4×Dic5D1211yescharacteristic
189C4×Dic5C22×D311yescharacteristic
190C2×#168C22×D312yes—
191C8×D5—24no—
192#533—151no—
193#532—151no—
194#488—154no—
195#487—151no—
196#487—151no—
197#486—31no—
198#486—151no—
199#416—154no—
200C2×C4×C8—51no—
201C22×C3×C5C22×D411yescharacteristic
202C2×C5×D3—42no—
203C2×C5×D3—42no—
204C2×C5×D3—42no—
205C2×C3×D5—21no—
206C2×C3×D5—21no—
207C2×C3×D5#12412yes—
208C3×C4×C5#13512yes—
209C3×C4×C5#13512yes—
210C3×C4×C5C2×#4112yes—
211Dic15—42no—
212Dic15—42no—
213C3×Dic5—21no—
214C3×Dic5—21no—
215C3×Dic5#12412yes—
216C5×Dic3—42no—
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—51no—
220C2×#67—102no—
221#235—108no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12C22×D512yes—
225C2×C4×D3—102no—
226C2×Dic6—21no—
227C2×Dic6—52no—
228C2×Dic6—101no—
229C2×C3×C8—52no—
230C2×C3×C8—104no—
231C2×C3×C8C22×D512yes—
232C3×C42—51no—
233C3×C42—51no—
234C3×C42—51no—
235C3×C42C22×D511yescharacteristic
236#217—102no—
237(C2×D3)⋊C4—102no—
238(C2×D3)⋊C4—102no—
239C4⋊Dic3—21no—
240C4⋊Dic3—52no—
241C4⋊Dic3—101no—
242C4⋊Dic3—101no—
243C4⋊Dic3—101no—
244C4⋊Dic3C22×D512yes—
245Dic3⋊C4—102no—
246Dic3⋊C4—102no—
247C4×Dic3—102no—
248C23×C5—62no—
249C22×D5C2×D1211yescharacteristic
250C5×Q8—122no—
251C5×D4—64no—
252C5×D4—122no—
253C5×D4—122no—
254C2×C4×C5—62no—
255C2×C4×C5C2×D1211yescharacteristic
256C2×C4×C5C2×D1211yescharacteristic
257C2×C4×C5C23×D311yescharacteristic
258C22⋊D5—124no—
259C2×Dic5—62no—
260C2×Dic5—62no—
261C2×Dic5—124no—
262C2×Dic5C2×D1211yescharacteristic
263C2×Dic5C2×D1211yescharacteristic
264C2×Dic5C2×D1211yescharacteristic
265C4×D5—22no—
266C4×D5—22no—
267C4×D5#23514yes—
268Dic10—64no—
269Dic10—122no—
270C5×C8—22no—
271#168—22no—
272C2×#41—152no—
273C22×C8—52no—
274C4⋊Q8—31no—
275C4⋊Q8—151no—
276C4⋊Q8—151no—
277#127—31no—
278#125—152no—
279#124—152no—
280C22⋊Q8—301no—
281C22⋊Q8—301no—
282#121—301no—
283#121—301no—
284C4×Q8—301no—
285C4×Q8—301no—
286C4×D4—301no—
287C4×D4—301no—
288#117—152no—
289C2×C42—51no—
290#103—154no—
291#103—154no—
292#102—34no—
293#102—154no—
294C4×C8—52no—
295C4×C8—51no—
296C4×C8D3×D511yescharacteristic
297C2×C3×C5C2×#12411yescharacteristic
298C2×C3×C5C2×#13511yescharacteristic
299C2×C3×C5C2×#13511yescharacteristic
300C3×D5—22no—
301C5×D3—82no—
302C23×C3—51no—
303C22×D3—22no—
304C2×C3×C4—51no—
305C2×C3×C4—54no—
306C2×C3×C4—51no—
307C2×C3×C4—51no—
308C2×C3×C4—102no—
309C2×C3×C4—102no—
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4C23×D511yescharacteristic
313#67—204no—
314C2×Dic3—22no—
315C2×Dic3—102no—
316C2×Dic3—102no—
317D12—24no—
318D12—42no—
319D12—42no—
320C4×D3—204no—
321Dic6—42no—
322Dic6—104no—
323Dic6—202no—
324C3×C8—22no—
325C3×C8—102no—
326C22×C5—122no—
327C22×C5—122no—
328C22×C5—122no—
329C22×C5C22×D1211yescharacteristic
330C2×D5—21no—
331C2×D5—21no—
332C2×D5#87512yes—
333C4×C5—122no—
334C4×C5#90412yes—
335C4×C5#90412yes—
336C4×C5C2×#23512yes—
337Dic5—21no—
338Dic5—21no—
339Dic5—122no—
340Dic5—122no—
341Dic5#87512yes—
342#41—308no—
343C2×Q8—61no—
344C2×Q8—152no—
345C2×Q8—301no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—302no—
350C22×C4—51no—
351C22×C4—51no—
352C22×C4—51no—
353C22×C4—302no—
354C2×C8—52no—
355C2×C8—104no—
356C2×C8C2×D3×D512yes—
357C4⋊C4—32no—
358C4⋊C4—61no—
359C4⋊C4—152no—
360C4⋊C4—302no—
361C4⋊C4—302no—
362C4⋊C4—301no—
363C4⋊C4—301no—
364C4⋊C4—301no—
365C22⋊C4—302no—
366C22⋊C4—302no—
367C22⋊C4—302no—
368C42—51no—
369C42—51no—
370C42—51no—
371C42—302no—
372C42C2×D3×D511yescharacteristic
373C3×C5#313111yescharacteristic, complemented, Hall
374C22×C3—52no—
375C22×C3—101no—
376C22×C3—101no—
377C22×C3C2×D4×D511yescharacteristic
378C2×D3—42no—
379C2×D3—42no—
380C2×D3—42no—
381C3×C4—52no—
382C3×C4—101no—
383C3×C4—101no—
384C3×C4#405812yes—
385C3×C4#406212yes—
386C3×C4D5×#4112yes—
387Dic3—42no—
388Dic3—202no—
389Dic3—202no—
390C2×C5—242no—
391C2×C5C2×#87511yescharacteristic
392C2×C5C2×#90411yescharacteristic
393C2×C5C2×#90411yescharacteristic
394D5—22no—
395C23—51no—
396C23—62no—
397Q8—122no—
398Q8—304no—
399Q8—602no—
400D4—64no—
401D4—122no—
402D4—122no—
403D4—604no—
404C2×C4—51no—
405C2×C4—54no—
406C2×C4—51no—
407C2×C4—51no—
408C2×C4—62no—
409C2×C4—102no—
410C2×C4—102no—
411C2×C4—302no—
412C2×C4—302no—
413C2×C4—604no—
414C2×C4D5×D1211yescharacteristic
415C2×C4D5×D1211yescharacteristic
416C2×C4C22×D3×D511yescharacteristic
417C8—22no—
418C8—102no—
419C2×C3—102no—
420C2×C3D5×#12411yescharacteristic
421C2×C3C2×#405811yescharacteristic
422C2×C3C2×#406211yescharacteristic
423D3—82no—
424C5#7846311yescharacteristic, complemented, Sylow
425C22—52no—
426C22—101no—
427C22—101no—
428C22—122no—
429C22—122no—
430C22—122no—
431C22C2×D5×D1211yescharacteristic
432C4—52no—
433C4—101no—
434C4—101no—
435C4—122no—
436C4—602no—
437C4—602no—
438C4#9126912yes—
439C4#9127012yes—
440C4D5×#23512yes—
441C3#1061329311yescharacteristic, complemented, Sylow
442C2—102no—
443C2—242no—
444C2D5×#87511yescharacteristic
445C2C2×#9126911yescharacteristic
446C2C2×#9127011yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11752672C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#3131
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11752506C2semidirect
3. #11750782C2semidirect
4. C5×#4694C2semidirect
5. C3×C4×C8×D5C2semidirect
6. #11748135C2semidirect
7. #11747963C2semidirect
8. #11746930C2semidirect
9. #11746906C2semidirect
44. C4×C8×D5D3semidirect
83. #4694D5semidirect
373. C3×C5#3131semidirect
424. C5#78463semidirect
441. C3#10613293semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117526722
#117525062
#117507822
C5×#46942
C3×C4×C8×D52
#117481352
#117479632
#117469302
#117469062
#106132933
#784635